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## Homework Statement

Given,

[tex]

{{(x - 7)}^{2}} + {{(y - 3)}^{2}} = {{8}^{2}}

[/tex]

What is,

[tex]

max(3x+4y)

[/tex]

## Homework Equations

None really.

## The Attempt at a Solution

Letting,

[tex]

3x+4y = C

[/tex]

When I get to the point where I have,

[tex]

{y} = {{\frac{-3x}{4}}+{\frac{C}{4}}}

[/tex]

Then substitute that in to,

[tex]

{{(x-7)}^{2}} + {{(y-3)}^{2}} = {{8}^{2}}

[/tex]

I get,

[tex]

{{\left(x - 7\right)}^{2}} + {{\left({\left({{\frac { - 3x}{4}} + {\frac {C}{4}}}\right)} - 3\right)}^{2}} = {{8}^{2}}

[/tex]

However, I am not sure how to proceed from here since I have two unknowns: [itex]x[/itex] and [tex]C[/tex].

So, how do I proceed from here?

Thanks,

-PFStudent

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